Topological and functional analytic properties of the compact--open topology on

In this paper, we study extensively the compact- G δ -open topology on the set C ( X ) of all real-valued continuous functions on a Tychonoff space X. In particular, we study the induced map, submetrizability, completeness properties, countability properties, and nuclear and reflexive properties of the compact- G δ -open topology on C ( X ) .